Lumatone mapping for 18edo: Difference between revisions

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As the highest edo with no diatonic or antidiatonic scale at all, this is a special case that needs its own intro and expansion on how to best span it.
ArrowHead294 (talk | contribs)
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There are many conceivable ways to map [[18edo]] onto the onto the Lumatone keyboard. However, it has no generators that create a diatonic or antidiatonic scale that covers the whole gamut, so the [[Standard Lumatone mapping for Pythagorean]] is not one of them. Due to its composite nature, only two generators work at all to produce single period mos scales.
{{Lumatone mapping intro}} Only two generators work at all to produce single-period mos scales.


== Wide fifth ==
== Wide fifth ==
7/18 produces a [[5L 3s]]-based Jankó mapping.
7\18 produces a [[5L 3s]]-based Jankó mapping.
{{Lumatone EDO mapping|n=18|start=0|xstep=3|ystep=-2}}
{{Lumatone EDO mapping|n=18|start=0|xstep=3|ystep=-2}}


This can be compressed down to a [[2L 1s]] mapping that is useful for maximising range.


This can be compressed down to a [[2L 1s]] mapping that is useful for maximising range.
{{Lumatone EDO mapping|n=18|start=16|xstep=7|ystep=-3}}
{{Lumatone EDO mapping|n=18|start=16|xstep=7|ystep=-3}}


== Flat neutral thirds ==
== Flat neutral thirds ==
5/18 produces a [[4L 3s]]-based Jankó mapping.
5\18 produces a [[4L 3s]]-based Jankó mapping.
{{Lumatone EDO mapping|n=18|start=0|xstep=3|ystep=-1}}
{{Lumatone EDO mapping|n=18|start=0|xstep=3|ystep=-1}}


This can also be compressed down to a [[3L 1s]] mapping that is useful if you want to keep octaves as close to horizontal as possible.


This can also be compressed down to a [[3L 1s]] mapping that is useful if you want to keep octaves as close to horizontal as possible.
{{Lumatone EDO mapping|n=18|start=16|xstep=5|ystep=-2}}
{{Lumatone EDO mapping|n=18|start=16|xstep=5|ystep=-2}}


{{Navbox Lumatone}}
{{Navbox Lumatone}}

Revision as of 16:47, 26 March 2025

There are many conceivable ways to map 18edo onto the onto the Lumatone keyboard. However, as both of its fifths are about as far away from just as possible, neither the sharp or the flat versions of the Standard Lumatone mapping for Pythagorean work particularly well. Only two generators work at all to produce single-period mos scales.

Wide fifth

7\18 produces a 5L 3s-based Jankó mapping.

0
3
1
4
7
10
13
17
2
5
8
11
14
17
2
0
3
6
9
12
15
0
3
6
9
12
16
1
4
7
10
13
16
1
4
7
10
13
16
1
17
2
5
8
11
14
17
2
5
8
11
14
17
2
5
8
11
15
0
3
6
9
12
15
0
3
6
9
12
15
0
3
6
9
12
15
0
16
1
4
7
10
13
16
1
4
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13
16
1
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10
13
16
1
4
7
10
14
17
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5
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14
17
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5
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14
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5
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14
17
2
5
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14
17
0
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12
15
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3
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12
15
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3
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12
15
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3
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3
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10
13
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1
4
7
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13
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1
4
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13
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1
4
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10
13
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1
4
7
10
17
2
5
8
11
14
17
2
5
8
11
14
17
2
5
8
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14
17
2
5
8
11
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9
12
15
0
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6
9
12
15
0
3
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12
15
0
3
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9
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4
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10
13
16
1
4
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10
13
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1
4
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10
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14
17
2
5
8
11
14
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5
8
15
0
3
6
9
12
15
0
3
6
9
4
7
10
13
16
1
4
7
14
17
2
5
8
3
6


This can be compressed down to a 2L 1s mapping that is useful for maximising range.

16
5
2
9
16
5
12
17
6
13
2
9
16
5
12
3
10
17
6
13
2
9
16
5
12
1
0
7
14
3
10
17
6
13
2
9
16
5
12
1
4
11
0
7
14
3
10
17
6
13
2
9
16
5
12
1
8
1
8
15
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11
0
7
14
3
10
17
6
13
2
9
16
5
12
1
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5
12
1
8
15
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11
0
7
14
3
10
17
6
13
2
9
16
5
12
1
8
15
2
9
16
5
12
1
8
15
4
11
0
7
14
3
10
17
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13
2
9
16
5
12
1
8
15
13
2
9
16
5
12
1
8
15
4
11
0
7
14
3
10
17
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13
2
9
16
5
12
1
8
15
4
13
2
9
16
5
12
1
8
15
4
11
0
7
14
3
10
17
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13
2
9
16
5
12
1
8
2
9
16
5
12
1
8
15
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11
0
7
14
3
10
17
6
13
2
9
16
5
12
2
9
16
5
12
1
8
15
4
11
0
7
14
3
10
17
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13
2
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9
16
5
12
1
8
15
4
11
0
7
14
3
10
17
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9
16
5
12
1
8
15
4
11
0
7
14
3
10
16
5
12
1
8
15
4
11
0
7
14
16
5
12
1
8
15
4
11
5
12
1
8
15
5
12

Flat neutral thirds

5\18 produces a 4L 3s-based Jankó mapping.

0
3
2
5
8
11
14
1
4
7
10
13
16
1
4
3
6
9
12
15
0
3
6
9
12
15
2
5
8
11
14
17
2
5
8
11
14
17
2
5
4
7
10
13
16
1
4
7
10
13
16
1
4
7
10
13
16
3
6
9
12
15
0
3
6
9
12
15
0
3
6
9
12
15
0
3
6
5
8
11
14
17
2
5
8
11
14
17
2
5
8
11
14
17
2
5
8
11
14
17
4
7
10
13
16
1
4
7
10
13
16
1
4
7
10
13
16
1
4
7
10
13
16
1
4
7
9
12
15
0
3
6
9
12
15
0
3
6
9
12
15
0
3
6
9
12
15
0
3
6
9
12
15
0
17
2
5
8
11
14
17
2
5
8
11
14
17
2
5
8
11
14
17
2
5
8
11
14
17
2
10
13
16
1
4
7
10
13
16
1
4
7
10
13
16
1
4
7
10
13
16
1
4
0
3
6
9
12
15
0
3
6
9
12
15
0
3
6
9
12
15
0
3
11
14
17
2
5
8
11
14
17
2
5
8
11
14
17
2
5
1
4
7
10
13
16
1
4
7
10
13
16
1
4
12
15
0
3
6
9
12
15
0
3
6
2
5
8
11
14
17
2
5
13
16
1
4
7
3
6


This can also be compressed down to a 3L 1s mapping that is useful if you want to keep octaves as close to horizontal as possible.

16
3
1
6
11
16
3
17
4
9
14
1
6
11
16
2
7
12
17
4
9
14
1
6
11
16
0
5
10
15
2
7
12
17
4
9
14
1
6
11
3
8
13
0
5
10
15
2
7
12
17
4
9
14
1
6
11
1
6
11
16
3
8
13
0
5
10
15
2
7
12
17
4
9
14
1
6
4
9
14
1
6
11
16
3
8
13
0
5
10
15
2
7
12
17
4
9
14
1
6
2
7
12
17
4
9
14
1
6
11
16
3
8
13
0
5
10
15
2
7
12
17
4
9
14
1
10
15
2
7
12
17
4
9
14
1
6
11
16
3
8
13
0
5
10
15
2
7
12
17
4
9
14
1
5
10
15
2
7
12
17
4
9
14
1
6
11
16
3
8
13
0
5
10
15
2
7
12
17
4
5
10
15
2
7
12
17
4
9
14
1
6
11
16
3
8
13
0
5
10
15
2
7
0
5
10
15
2
7
12
17
4
9
14
1
6
11
16
3
8
13
0
5
0
5
10
15
2
7
12
17
4
9
14
1
6
11
16
3
8
13
0
5
10
15
2
7
12
17
4
9
14
1
6
13
0
5
10
15
2
7
12
17
4
9
8
13
0
5
10
15
2
7
8
13
0
5
10
3
8


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